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C $Header: /u/gcmpack/MITgcm/pkg/generic_advdiff/gad_som_adv_r.F,v 1.8 2013/03/02 00:39:47 jmc Exp $ |
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C $Name: $ |
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|
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#include "GAD_OPTIONS.h" |
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|
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CBOP |
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C !ROUTINE: GAD_SOM_ADV_R |
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|
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C !INTERFACE: ========================================================== |
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SUBROUTINE GAD_SOM_ADV_R( |
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I bi,bj,k, kUp, kDw, |
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I deltaTloc, rTrans, maskUp, maskIn, |
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U sm_v, sm_o, sm_x, sm_y, sm_z, |
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U sm_xx, sm_yy, sm_zz, sm_xy, sm_xz, sm_yz, |
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U alp, aln, fp_v, fn_v, fp_o, fn_o, |
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U fp_x, fn_x, fp_y, fn_y, fp_z, fn_z, |
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U fp_xx, fn_xx, fp_yy, fn_yy, fp_zz, fn_zz, |
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U fp_xy, fn_xy, fp_xz, fn_xz, fp_yz, fn_yz, |
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O wT, |
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I myThid ) |
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|
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C !DESCRIPTION: |
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C Calculates the area integrated vertical flux due to advection |
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C of a tracer using |
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C-- |
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C Second-Order Moments Advection of tracer in Z-direction |
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C ref: M.J.Prather, 1986, JGR, 91, D6, pp 6671-6681. |
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C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----| |
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C The 3-D grid has dimension (Nx,Ny,Nz) with corresponding |
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C velocity field (U,V,W). Parallel subroutine calculate |
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C advection in the X- and Y- directions. |
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C The moment [Si] are as defined in the text, Sm refers to |
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C the total mass in each grid box |
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C the moments [Fi] are similarly defined and used as temporary |
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C storage for portions of the grid boxes in transit. |
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C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----| |
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|
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C !USES: =============================================================== |
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IMPLICIT NONE |
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#include "SIZE.h" |
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#include "EEPARAMS.h" |
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#include "PARAMS.h" |
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#include "GRID.h" |
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#include "GAD.h" |
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|
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C !INPUT PARAMETERS: =================================================== |
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C bi,bj :: tile indices |
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C k :: vertical level |
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C kUp :: index into 2 1/2D array, toggles between 1 and 2 |
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C kDw :: index into 2 1/2D array, toggles between 2 and 1 |
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C rTrans :: vertical volume transport |
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C maskUp :: 2-D array mask for W points |
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C maskIn :: 2-D array Interior mask |
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C myThid :: my Thread Id. number |
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INTEGER bi,bj,k, kUp, kDw |
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_RL deltaTloc |
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_RL rTrans(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RS maskUp(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RS maskIn(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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INTEGER myThid |
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|
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C !OUTPUT PARAMETERS: ================================================== |
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C sm_v :: volume of grid cell |
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C sm_o :: tracer content of grid cell (zero order moment) |
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C sm_x,y,z :: 1rst order moment of tracer distribution, in x,y,z direction |
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C sm_xx,yy,zz :: 2nd order moment of tracer distribution, in x,y,z direction |
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C sm_xy,xz,yz :: 2nd order moment of tracer distr., in cross direction xy,xz,yz |
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C wT :: vertical advective flux |
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_RL sm_v (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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_RL sm_o (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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_RL sm_x (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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_RL sm_y (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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_RL sm_z (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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_RL sm_xx (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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_RL sm_yy (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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_RL sm_zz (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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_RL sm_xy (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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_RL sm_xz (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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_RL sm_yz (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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_RL alp (1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) |
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_RL aln (1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) |
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_RL fp_v (1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) |
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_RL fn_v (1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) |
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_RL fp_o (1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) |
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_RL fn_o (1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) |
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_RL fp_x (1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) |
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_RL fn_x (1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) |
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_RL fp_y (1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) |
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_RL fn_y (1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) |
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_RL fp_z (1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) |
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_RL fn_z (1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) |
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_RL fp_xx(1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) |
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_RL fn_xx(1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) |
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_RL fp_yy(1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) |
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_RL fn_yy(1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) |
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_RL fp_zz(1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) |
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_RL fn_zz(1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) |
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_RL fp_xy(1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) |
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_RL fn_xy(1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) |
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_RL fp_xz(1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) |
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_RL fn_xz(1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) |
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_RL fp_yz(1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) |
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_RL fn_yz(1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) |
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_RL wT (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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|
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C !LOCAL VARIABLES: ==================================================== |
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C i,j :: loop indices |
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C wLoc :: volume transported (per time step) |
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_RL three |
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PARAMETER( three = 3. _d 0 ) |
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INTEGER i,j |
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INTEGER km1 |
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LOGICAL noFlowAcrossSurf |
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_RL recip_dT |
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_RL wLoc, alf1, alf1q, alpmn |
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_RL alfp, alpq, alp1, locTp |
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_RL alfn, alnq, aln1, locTn |
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CEOP |
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|
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#ifdef ALLOW_AUTODIFF |
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alp(1,1,kDw) = alp(1,1,kDw) |
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aln(1,1,kDw) = aln(1,1,kDw) |
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fp_v(1,1,kDw) = fp_v(1,1,kDw) |
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fn_v(1,1,kDw) = fn_v(1,1,kDw) |
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fp_o(1,1,kDw) = fp_o(1,1,kDw) |
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fn_o(1,1,kDw) = fn_o(1,1,kDw) |
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fp_x(1,1,kDw) = fp_x(1,1,kDw) |
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fn_x(1,1,kDw) = fn_x(1,1,kDw) |
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fp_y(1,1,kDw) = fp_y(1,1,kDw) |
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fn_y(1,1,kDw) = fn_y(1,1,kDw) |
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fp_z(1,1,kDw) = fp_z(1,1,kDw) |
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fn_z(1,1,kDw) = fn_z(1,1,kDw) |
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fp_xx(1,1,kDw) = fp_xx(1,1,kDw) |
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fn_xx(1,1,kDw) = fn_xx(1,1,kDw) |
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fp_yy(1,1,kDw) = fp_yy(1,1,kDw) |
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fn_yy(1,1,kDw) = fn_yy(1,1,kDw) |
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fp_zz(1,1,kDw) = fp_zz(1,1,kDw) |
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fn_zz(1,1,kDw) = fn_zz(1,1,kDw) |
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fp_xy(1,1,kDw) = fp_xy(1,1,kDw) |
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fn_xy(1,1,kDw) = fn_xy(1,1,kDw) |
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fp_xz(1,1,kDw) = fp_xz(1,1,kDw) |
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fn_xz(1,1,kDw) = fn_xz(1,1,kDw) |
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fp_yz(1,1,kDw) = fp_yz(1,1,kDw) |
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fn_yz(1,1,kDw) = fn_yz(1,1,kDw) |
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#endif |
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|
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recip_dT = zeroRL |
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IF ( deltaTloc.GT.zeroRL ) recip_dT = 1.0 _d 0 / deltaTloc |
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noFlowAcrossSurf = rigidLid .OR. nonlinFreeSurf.GE.1 |
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& .OR. select_rStar.NE.0 |
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|
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C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----| |
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C--- part.1 : calculate flux for all moments |
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DO j=jMinAdvR,jMaxAdvR |
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DO i=iMinAdvR,iMaxAdvR |
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wLoc = rTrans(i,j)*deltaTloc |
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C-- Flux from (k) to (k-1) when W>0 (i.e., take upper side of box k) |
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C- note: Linear free surface case: this takes care of w_surf advection out |
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C of the domain since for this particular case, rTrans is not masked |
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fp_v (i,j,kUp) = MAX( zeroRL, wLoc ) |
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alp (i,j,kUp) = fp_v(i,j,kUp)/sm_v(i,j,k) |
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alpq = alp(i,j,kUp)*alp(i,j,kUp) |
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alp1 = 1. _d 0 - alp(i,j,kUp) |
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C- Create temporary moments/masses for partial boxes in transit |
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C use same indexing as velocity, "p" for positive W |
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fp_o (i,j,kUp) = alp(i,j,kUp)* |
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& ( sm_o(i,j, k ) + alp1*sm_z(i,j, k ) |
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& + alp1*(alp1-alp(i,j,kUp))*sm_zz(i,j, k ) |
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& ) |
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fp_z (i,j,kUp) = alpq* |
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& ( sm_z(i,j, k ) + three*alp1*sm_zz(i,j, k ) ) |
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fp_zz(i,j,kUp) = alp(i,j,kUp)*alpq*sm_zz(i,j, k ) |
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fp_x (i,j,kUp) = alp(i,j,kUp)* |
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& ( sm_x(i,j, k ) + alp1*sm_xz(i,j, k ) ) |
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fp_y (i,j,kUp) = alp(i,j,kUp)* |
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& ( sm_y(i,j, k ) + alp1*sm_yz(i,j, k ) ) |
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fp_xz(i,j,kUp) = alpq *sm_xz(i,j, k ) |
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fp_yz(i,j,kUp) = alpq *sm_yz(i,j, k ) |
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fp_xx(i,j,kUp) = alp(i,j,kUp)*sm_xx(i,j, k ) |
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fp_yy(i,j,kUp) = alp(i,j,kUp)*sm_yy(i,j, k ) |
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fp_xy(i,j,kUp) = alp(i,j,kUp)*sm_xy(i,j, k ) |
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ENDDO |
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ENDDO |
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IF ( k.EQ.1 ) THEN |
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C-- Linear free surface, calculate w_surf (<0) advection term |
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km1 = 1 |
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DO j=jMinAdvR,jMaxAdvR |
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DO i=iMinAdvR,iMaxAdvR |
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wLoc = rTrans(i,j)*deltaTloc |
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C- Flux from above to (k) when W<0 , surface case: |
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C take box k=1, assuming zero 1rst & 2nd moment in Z dir. |
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fn_v (i,j,kUp) = MAX( zeroRL, -wLoc ) |
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aln (i,j,kUp) = fn_v(i,j,kUp)/sm_v(i,j,km1) |
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alnq = aln(i,j,kUp)*aln(i,j,kUp) |
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aln1 = 1. _d 0 - aln(i,j,kUp) |
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C- Create temporary moments/masses for partial boxes in transit |
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C use same indexing as velocity, "n" for negative W |
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fn_o (i,j,kUp) = aln(i,j,kUp)*sm_o(i,j,km1) |
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fn_z (i,j,kUp) = zeroRL |
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fn_zz(i,j,kUp) = zeroRL |
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fn_x (i,j,kUp) = aln(i,j,kUp)*sm_x(i,j,km1) |
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fn_y (i,j,kUp) = aln(i,j,kUp)*sm_y(i,j,km1) |
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fn_xz(i,j,kUp) = zeroRL |
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fn_yz(i,j,kUp) = zeroRL |
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fn_xx(i,j,kUp) = aln(i,j,kUp)*sm_xx(i,j,km1) |
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fn_yy(i,j,kUp) = aln(i,j,kUp)*sm_yy(i,j,km1) |
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fn_xy(i,j,kUp) = aln(i,j,kUp)*sm_xy(i,j,km1) |
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C-- Save zero-order flux: |
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wT(i,j) = ( fp_o(i,j,kUp) - fn_o(i,j,kUp) )*recip_dT |
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ENDDO |
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ENDDO |
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ELSE |
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C-- Interior only: mask rTrans (if not already done) |
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km1 = k-1 |
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DO j=jMinAdvR,jMaxAdvR |
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DO i=iMinAdvR,iMaxAdvR |
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wLoc = maskUp(i,j)*rTrans(i,j)*deltaTloc |
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C- Flux from (k-1) to (k) when W<0 (i.e., take lower side of box k-1) |
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fn_v (i,j,kUp) = MAX( zeroRL, -wLoc ) |
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aln (i,j,kUp) = fn_v(i,j,kUp)/sm_v(i,j,km1) |
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alnq = aln(i,j,kUp)*aln(i,j,kUp) |
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aln1 = 1. _d 0 - aln(i,j,kUp) |
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C- Create temporary moments/masses for partial boxes in transit |
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C use same indexing as velocity, "n" for negative W |
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fn_o (i,j,kUp) = aln(i,j,kUp)* |
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& ( sm_o(i,j,km1) - aln1*sm_z(i,j,km1) |
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& + aln1*(aln1-aln(i,j,kUp))*sm_zz(i,j,km1) |
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& ) |
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fn_z (i,j,kUp) = alnq* |
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& ( sm_z(i,j,km1) - three*aln1*sm_zz(i,j,km1) ) |
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fn_zz(i,j,kUp) = aln(i,j,kUp)*alnq*sm_zz(i,j,km1) |
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fn_x (i,j,kUp) = aln(i,j,kUp)* |
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& ( sm_x(i,j,km1) - aln1*sm_xz(i,j,km1) ) |
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fn_y (i,j,kUp) = aln(i,j,kUp)* |
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& ( sm_y(i,j,km1) - aln1*sm_yz(i,j,km1) ) |
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fn_xz(i,j,kUp) = alnq *sm_xz(i,j,km1) |
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fn_yz(i,j,kUp) = alnq *sm_yz(i,j,km1) |
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fn_xx(i,j,kUp) = aln(i,j,kUp)*sm_xx(i,j,km1) |
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fn_yy(i,j,kUp) = aln(i,j,kUp)*sm_yy(i,j,km1) |
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fn_xy(i,j,kUp) = aln(i,j,kUp)*sm_xy(i,j,km1) |
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C-- Save zero-order flux: |
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wT(i,j) = ( fp_o(i,j,kUp) - fn_o(i,j,kUp) )*recip_dT |
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ENDDO |
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ENDDO |
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C-- end surface/interior cases for W<0 advective fluxes |
246 |
ENDIF |
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IF ( .NOT.uniformFreeSurfLev .AND. k.NE.1 .AND. |
248 |
& .NOT.noFlowAcrossSurf ) THEN |
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C-- Linear free surface, but surface not @ k=1 : |
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C calculate w_surf (<0) advection term from current level |
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C moments assuming zero 1rst & 2nd moment in Z dir. ; |
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C and add to previous fluxes; note: identical to resetting fluxes |
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C since previous fluxes are zero in this case (=> let TAF decide) |
254 |
km1 = k |
255 |
DO j=jMinAdvR,jMaxAdvR |
256 |
DO i=iMinAdvR,iMaxAdvR |
257 |
wLoc = rTrans(i,j)*deltaTloc |
258 |
IF ( k.EQ.kSurfC(i,j,bi,bj) ) THEN |
259 |
C- Flux from (k-1) to (k) when W<0 (special surface case, take box k) |
260 |
fn_v (i,j,kUp) = MAX( zeroRL, -wLoc ) |
261 |
aln (i,j,kUp) = fn_v(i,j,kUp)/sm_v(i,j,km1) |
262 |
C- Create temporary moments/masses for partial boxes in transit |
263 |
C use same indexing as velocity, "n" for negative W |
264 |
fn_o (i,j,kUp) = aln(i,j,kUp)*sm_o(i,j,km1) |
265 |
fn_x (i,j,kUp) = aln(i,j,kUp)*sm_x(i,j,km1) |
266 |
fn_y (i,j,kUp) = aln(i,j,kUp)*sm_y(i,j,km1) |
267 |
fn_xx(i,j,kUp) = aln(i,j,kUp)*sm_xx(i,j,km1) |
268 |
fn_yy(i,j,kUp) = aln(i,j,kUp)*sm_yy(i,j,km1) |
269 |
fn_xy(i,j,kUp) = aln(i,j,kUp)*sm_xy(i,j,km1) |
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C-- Save zero-order flux: |
271 |
wT(i,j) = ( fp_o(i,j,kUp) - fn_o(i,j,kUp) )*recip_dT |
272 |
ENDIF |
273 |
ENDDO |
274 |
ENDDO |
275 |
ENDIF |
276 |
|
277 |
C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----| |
278 |
C--- part.2 : re-adjust moments remaining in the box |
279 |
C take off from grid box (k): negative W(kDw) and positive W(kUp) |
280 |
DO j=jMinAdvR,jMaxAdvR |
281 |
DO i=iMinAdvR,iMaxAdvR |
282 |
#ifdef ALLOW_OBCS |
283 |
IF ( maskIn(i,j).NE.zeroRS ) THEN |
284 |
#endif /* ALLOW_OBCS */ |
285 |
alf1 = 1. _d 0 - aln(i,j,kDw) - alp(i,j,kUp) |
286 |
alf1q = alf1*alf1 |
287 |
alpmn = alp(i,j,kUp) - aln(i,j,kDw) |
288 |
sm_v (i,j,k) = sm_v (i,j,k) - fn_v (i,j,kDw) - fp_v (i,j,kUp) |
289 |
sm_o (i,j,k) = sm_o (i,j,k) - fn_o (i,j,kDw) - fp_o (i,j,kUp) |
290 |
sm_z (i,j,k) = alf1q*( sm_z(i,j,k) - three*alpmn*sm_zz(i,j,k) ) |
291 |
sm_zz(i,j,k) = alf1*alf1q*sm_zz(i,j,k) |
292 |
sm_xz(i,j,k) = alf1q*sm_xz(i,j,k) |
293 |
sm_yz(i,j,k) = alf1q*sm_yz(i,j,k) |
294 |
sm_x (i,j,k) = sm_x (i,j,k) - fn_x (i,j,kDw) - fp_x (i,j,kUp) |
295 |
sm_xx(i,j,k) = sm_xx(i,j,k) - fn_xx(i,j,kDw) - fp_xx(i,j,kUp) |
296 |
sm_y (i,j,k) = sm_y (i,j,k) - fn_y (i,j,kDw) - fp_y (i,j,kUp) |
297 |
sm_yy(i,j,k) = sm_yy(i,j,k) - fn_yy(i,j,kDw) - fp_yy(i,j,kUp) |
298 |
sm_xy(i,j,k) = sm_xy(i,j,k) - fn_xy(i,j,kDw) - fp_xy(i,j,kUp) |
299 |
#ifdef ALLOW_OBCS |
300 |
ENDIF |
301 |
#endif /* ALLOW_OBCS */ |
302 |
ENDDO |
303 |
ENDDO |
304 |
|
305 |
C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----| |
306 |
C--- part.3 : Put the temporary moments into appropriate neighboring boxes |
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C add into grid box (k): positive W(kDw) and negative W(kUp) |
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DO j=jMinAdvR,jMaxAdvR |
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DO i=iMinAdvR,iMaxAdvR |
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#ifdef ALLOW_OBCS |
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IF ( maskIn(i,j).NE.zeroRS ) THEN |
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#endif /* ALLOW_OBCS */ |
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sm_v (i,j,k) = sm_v (i,j,k) + fp_v (i,j,kDw) + fn_v (i,j,kUp) |
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alfp = fp_v(i,j,kDw)/sm_v(i,j,k) |
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alfn = fn_v(i,j,kUp)/sm_v(i,j,k) |
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alf1 = 1. _d 0 - alfp - alfn |
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alp1 = 1. _d 0 - alfp |
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aln1 = 1. _d 0 - alfn |
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alpmn = alfp - alfn |
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locTp = alfp*sm_o(i,j,k) - alp1*fp_o(i,j,kDw) |
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locTn = alfn*sm_o(i,j,k) - aln1*fn_o(i,j,kUp) |
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sm_zz(i,j,k) = alf1*alf1*sm_zz(i,j,k) + alfp*alfp*fp_zz(i,j,kDw) |
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& + alfn*alfn*fn_zz(i,j,kUp) |
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& - 5. _d 0*(-alpmn*alf1*sm_z(i,j,k) + alfp*alp1*fp_z(i,j,kDw) |
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& - alfn*aln1*fn_z(i,j,kUp) |
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& + twoRL*alfp*alfn*sm_o(i,j,k) + (alp1-alfp)*locTp |
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& + (aln1-alfn)*locTn |
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& ) |
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sm_xz(i,j,k) = alf1*sm_xz(i,j,k) + alfp*fp_xz(i,j,kDw) |
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& + alfn*fn_xz(i,j,kUp) |
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& + three*( alpmn*sm_x(i,j,k) - alp1*fp_x(i,j,kDw) |
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& + aln1*fn_x(i,j,kUp) |
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& ) |
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sm_yz(i,j,k) = alf1*sm_yz(i,j,k) + alfp*fp_yz(i,j,kDw) |
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& + alfn*fn_yz(i,j,kUp) |
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& + three*( alpmn*sm_y(i,j,k) - alp1*fp_y(i,j,kDw) |
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& + aln1*fn_y(i,j,kUp) |
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& ) |
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sm_z (i,j,k) = alf1*sm_z(i,j,k) + alfp*fp_z(i,j,kDw) |
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& + alfn*fn_z(i,j,kUp) |
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& + three*( locTp - locTn ) |
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sm_o (i,j,k) = sm_o (i,j,k) + fp_o (i,j,kDw) + fn_o (i,j,kUp) |
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sm_x (i,j,k) = sm_x (i,j,k) + fp_x (i,j,kDw) + fn_x (i,j,kUp) |
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sm_xx(i,j,k) = sm_xx(i,j,k) + fp_xx(i,j,kDw) + fn_xx(i,j,kUp) |
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sm_y (i,j,k) = sm_y (i,j,k) + fp_y (i,j,kDw) + fn_y (i,j,kUp) |
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sm_yy(i,j,k) = sm_yy(i,j,k) + fp_yy(i,j,kDw) + fn_yy(i,j,kUp) |
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sm_xy(i,j,k) = sm_xy(i,j,k) + fp_xy(i,j,kDw) + fn_xy(i,j,kUp) |
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#ifdef ALLOW_OBCS |
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ENDIF |
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#endif /* ALLOW_OBCS */ |
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ENDDO |
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ENDDO |
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|
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RETURN |
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END |